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Yes. Take the functions
f(x) = log(x)
or
g(x) = ln(x)
In both cases, there is a vertical asymptote where x = 0. Because a number cannot be taken to any power so that it equals zero, and can only come closer and closer to zero without actually reaching it, there is an asymptote where it would equal zero. Note that transformations (especially shifting the function left and right) can change the properties of this asymptote.
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Which trigonometric functions have asymptotes?
tangent, cosecants, secant, cotangent.
Why are asymptotes important characteristics of rational functions?
Asymptotes are one way - not the only way, but one of several - to analyze the general behavior of a function.
A sign chart helps you record data about a function's values around its and asymptotes?
A sign chart helps you record data about a function's values around its _____ and _____ asymptotes. zeros vertical
What is the difference between exponential functions and logarithmic functions?
Exponential and logarithmic functions are different in so far as each is interchangeable with the other depending on how the numbers in a problem are expressed. It is simple to translate exponential equations into logarithmic functions with the aid of certain principles.
How are exponential and logarithmic functions related?
They are inverses of each other.
What are the three types of asymptotes?
Three types of asymptotes are oblique/slant, horizontal, and vertical
What are the slopes of the hyperbola's asymptotes?
If a hyperbola is vertical, the asymptotes have a slope of m = +- a/b. If a hyperbola is horizontal, the asymptotes have a slope of m = +- b/a.
How many vertical asymptotes does the graph of this function have?
2
What is the vertical asymptotes for tan2x?
there is non its an infinite line.
The vertical of the function secant are determined by the points that are not in the domain?
Asymptotes
How do you find vertical asymptotes for trig functions?
Only the cofunctions have asymptotes. Because csc x = 1/sin x, csc x has vertical asymptotes whenever the denominator is equal to 0, or whenever sin x = 0, which are the multiples of pi (0,1,2,3,4,...). For sec x, it's 1/cos x, thus cos x = 0, x = pi/2 + pi*n, where n is a counting number (0,1,2,etc...). cot x = cos x/sin x, thus its vertical asymptotes are the same as those of csc x. If the function is transformed, look at the number in front of x (for example, csc (2x), that number would be 2)), and divide the fundamental asymptotes (above) by that number. The vertical asymptotes of csc (2x) would be (pi/2, 2pi/2, 3pi/2, etc...).
Can a rational function have no vertical horizontal oblique asymptotes?
No, it will always have one.
What is the relationship between exponential and logarithmic functions?
Exponential and logarithmic functions are inverses of each other.
How do you find horizontal and vertical asymptotes?
finding vertical asymptotes is easy. lets use the equation y = (2x-2)/((x^2)-2x-3) since its a rational equation, all we have to do to find the vertical asymptotes is find the values at which the denominator would be equal to 0. since this makes it an undefined equation, that is where the asymptotes are. for this equation, -1 and 3 are the answers for the vertical ayspmtotes. the horizontal asymptotes are a lot more tricky. to solve them, simplify the equation if it is in factored form, then divide all terms both in the numerator and denominator with the term with the highest degree. so the horizontal asymptote of this equation is 0.
How many non-verticle asymptotes can a rational function have?
Not sure what non-verticle means, but a rational function can have up to 2 non-vertical asymptotes,
Which trigonometric functions have asymptotes?
tangent, cosecants, secant, cotangent.
Why are asymptotes important characteristics of rational functions?
Asymptotes are one way - not the only way, but one of several - to analyze the general behavior of a function.
